Anisotropic skyrmion mass induced by conduction electrons: a Schwinger-Keldysh functional integral approach*

The current-driven motion of skyrmions in magnetic materials, as topologically protected winding vector fields of local magnetization, has attracted considerable attention due to both fundamental interest in dynamics of topological solitons and potential spintronic applications. While long-established Thiele equations capture its rigid motion [1] under the assumption of preserved skyrmion shape, experiments on realistic skyrmions [2] find deviation due to inertial mass which has been explained theoretically as the consequence of their internal dynamics [1, 3], geometry of the nanowire [4], and interactions with magnons [5] or phonons [6]. However, experimentally observed skyrmion mass is often much much larger than predicted by existing theories. In this study, we employ Schwinger-Keldysh functional integral approach to study electrons interacting with localized magnetic moments to obtain a stochastic equation of motion for skyrmions whose time-retarded damping kernel contains new anisotropic mass term generated by conduction electrons. 

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[2] F. Büttner et al., Nat. Phys. 11, 225 (2015).

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[4] A. Pavlis and C. Psaroudaki, Phys. Rev. Res. 2, 032058(R) (2020).

[5] C. Psaroudaki and D. Loss, Phys. Rev. Lett. 120, 237203 (2018).

[6] D. Capic, E. M. Chudnovsky and D. A. Garanin, Phys. Rev. B 102, 060404(R) (2020).